Appendix-E-Ensemble-Kalman-Filters.ipynb

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    "[Table of Contents](http://nbviewer.ipython.org/github/rlabbe/Kalman-and-Bayesian-Filters-in-Python/blob/master/table_of_contents.ipynb)"
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   "source": [
    "# Ensemble Kalman Filters"
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   "source": [
    "#format the book\n",
    "%matplotlib inline\n",
    "from __future__ import division, print_function\n",
    "from book_format import load_style\n",
    "load_style()"
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   "source": [
    "> I am not well versed with Ensemble filters. I have implemented one for this book, and made it work, but I have not used one in real life. Different sources use slightly different forms of these equations. If I implement the equations given in the sources the filter does not work. It is possible that I am doing something wrong. However, in various places on the web I have seen comments by people stating that they do the kinds of things I have done in my filter to make it work. In short, I do not understand this topic well, but choose to present my lack of knowledge rather than to gloss over the subject. I hope to master this topic in the future and to author a more definitive chapter. At the end of the chapter I document my current confusion and questions. In any case if I got confused by the sources perhaps you also will, so documenting my confusion can help you avoid the same.\n",
    "\n",
    "\n",
    "The ensemble Kalman filter (EnKF) is very similar to the unscented Kalman filter (UKF) of the last chapter. If you recall, the UKF uses a set of deterministically chosen weighted sigma points passed through nonlinear state and measurement functions. After the sigma points are passed through the function, we find the mean and covariance of the points and use this as the filter's new mean and covariance. It is only an approximation of the true value, and thus suboptimal, but in practice the filter is highly accurate. It has the advantage of often producing more accurate estimates than the EKF does, and also does not require you to analytically derive the linearization of the state and measurement equations. \n",
    "\n",
    "The ensemble Kalman filter works in a similar way, except it uses a *Monte Carlo* method to choose a large numbers of sigma points. It came about from the geophysical sciences as an answer for the very large states and systems needed to model things such as the ocean and atmosphere. There is an interesting article on it's development in weather modeling in *SIAM News* [1]. The filter starts by randomly generating a large number of points distributed about the filter's initial state. This distribution is proportional to the filter's covariance $\\mathbf{P}$. In other words 68% of the points will be within one standard deviation of the mean, 95% percent within two standard deviations, and so on. Let's look at this in two dimensions. We will use `numpy.random.multivariate_normal()` function to randomly create points from a multivariate normal distribution drawn from the mean (5, 3) with the covariance\n",
    "\n",
    "$$\\begin{bmatrix}\n",
    "32 & 15 \\\\ 15 & 40\n",
    "\\end{bmatrix}$$\n",
    "\n",
    "I've drawn the covariance ellipse representing two standard deviations to illustrate how the points are distributed."
   ]
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ZQfl0EK6hgAJbV2Sx3YCUpc/bQvN85gbYe4+PnTnkukDN/JsxN+NfdkNAAnohxNUhAb0Q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\nMaEnIiIiIkpj/w9PHoPvakSIMgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24e99b0a9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from numpy.random import multivariate_normal\n",
    "from filterpy.stats import (covariance_ellipse, \n",
    "                            plot_covariance_ellipse)\n",
    "\n",
    "mean = (5, 3)\n",
    "P = np.array([[32, 15],\n",
    "              [15., 40.]])\n",
    "\n",
    "x,y = multivariate_normal(mean=mean, cov=P, size=2500).T\n",
    "plt.scatter(x, y, alpha=0.3, marker='.')\n",
    "plt.axis('equal')\n",
    "\n",
    "plot_covariance_ellipse(mean=mean, cov=P,\n",
    "                        variance=2.**2,\n",
    "                        facecolor='none')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As I already stated, when the filter is initialized a large number of sigma points are drawn from the initial state ($\\mathbf{x}$) and covariance ($\\mathbf{P}$). From there the algorithm proceeds very similarly to the UKF. During the prediction step the sigma points are passed through the state transition function, and then perturbed by adding a bit of noise to account for the process noise. During the update step the sigma points are translated into measurement space by passing them through the measurement function, they are perturbed by a small amount to account for the measurement noise. The Kalman gain is computed from the \n",
    "\n",
    "We already mentioned the main difference between the UKF and EnKF - the UKF choses the sigma points deterministically. There is another difference, implied by the algorithm above. With the UKF we generate new sigma points during each predict step, and after passing the points through the nonlinear function we reconstitute them into a mean and covariance by using the *unscented transform*. The EnKF keeps propagating the originally created sigma points; we only need to compute a mean and covariance as outputs for the filter! \n",
    "\n",
    "Let's look at the equations for the filter. As usual, I will leave out the typical subscripts and superscripts; I am expressing an algorithm, not mathematical functions. Here $N$ is the number of sigma points, $\\chi$ is the set of sigma points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialize Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\boldsymbol\\chi \\sim \\mathcal{N}(\\mathbf{x}_0, \\mathbf{P}_0)$$\n",
    "\n",
    "This says to select the sigma points from the filter's initial mean and covariance. In code this might look like\n",
    "\n",
    "```python\n",
    "N = 1000\n",
    "sigmas = multivariate_normal(mean=x, cov=P, size=N)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predict Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{aligned}\n",
    "\\boldsymbol\\chi &= f(\\boldsymbol\\chi, \\mathbf{u}) + v_Q \\\\\n",
    "\\mathbf{x} &= \\frac{1}{N} \\sum_1^N \\boldsymbol\\chi\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "That is short and sweet, but perhaps not entirely clear. The first line passes all of the sigma points through a use supplied state transition function and then adds some noise distributed according to the $\\mathbf{Q}$ matrix. In Python we might write\n",
    "\n",
    "```python\n",
    "for i, s in enumerate(sigmas):\n",
    "    sigmas[i] = fx(x=s, dt=0.1, u=0.)\n",
    "\n",
    "sigmas += multivariate_normal(x, Q, N)\n",
    "```\n",
    "\n",
    "The second line computes the mean from the sigmas. In Python we will take advantage of `numpy.mean` to do this very concisely and quickly.\n",
    "\n",
    "```python\n",
    "x = np.mean(sigmas, axis=0)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now optionally compute the covariance of the mean. The algorithm does not need to compute this value, but it is often useful for analysis. The equation is\n",
    "\n",
    "$$\\mathbf{P} = \\frac{1}{N-1}\\sum_1^N[\\boldsymbol\\chi-\\mathbf{x}^-][\\boldsymbol\\chi-\\mathbf{x}^-]^\\mathsf{T}$$\n",
    "\n",
    "$\\boldsymbol\\chi-\\mathbf{x}^-$ is a one dimensional vector, so we will use `numpy.outer` to compute the $[\\boldsymbol\\chi-\\mathbf{x}^-][\\boldsymbol\\chi-\\mathbf{x}^-]^\\mathsf{T}$ term. In Python we might write\n",
    "\n",
    "```python\n",
    "    P = 0\n",
    "    for s in sigmas:\n",
    "        P += outer(s-x, s-x)\n",
    "    P = P / (N-1)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Update Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the update step we pass the sigma points through the measurement function, compute the mean and covariance of the sigma points, compute the Kalman gain from the covariance, and then update the Kalman state by scaling the residual by the Kalman gain. The equations are\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\boldsymbol\\chi_h &= h(\\boldsymbol\\chi, u)\\\\\n",
    "\\mathbf{z}_{mean} &= \\frac{1}{N}\\sum_1^N \\boldsymbol\\chi_h \\\\ \\\\\n",
    "\\mathbf{P}_{zz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi_h - \\mathbf{z}_{mean}][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} + \\mathbf{R} \\\\\n",
    "\\mathbf{P}_{xz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi - \\mathbf{x}^-][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} \\\\\n",
    "\\\\\n",
    "\\mathbf{K} &= \\mathbf{P}_{xz} \\mathbf{P}_{zz}^{-1}\\\\ \n",
    "\\boldsymbol\\chi & = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R] \\\\ \\\\\n",
    "\\mathbf{x} &= \\frac{1}{N} \\sum_1^N \\boldsymbol\\chi \\\\\n",
    "\\mathbf{P} &= \\mathbf{P} - \\mathbf{KP}_{zz}\\mathbf{K}^\\mathsf{T}\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is very similar to the linear KF and the UKF. Let's just go line by line.\n",
    "\n",
    "The first line,\n",
    "\n",
    "$$\\boldsymbol\\chi_h = h(\\boldsymbol\\chi, u),$$\n",
    "\n",
    "just passes the sigma points through the measurement function $h$. We name the resulting points $\\chi_h$ to distinguish them from the sigma points. In Python we could write this as\n",
    "\n",
    "```python\n",
    "sigmas_h = h(sigmas, u)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next line computes the mean of the measurement sigmas.\n",
    "\n",
    "$$\\mathbf{z}_{mean} = \\frac{1}{N}\\sum_1^N \\boldsymbol\\chi_h$$\n",
    "\n",
    "In Python we write\n",
    "\n",
    "```python\n",
    "z_mean = np.mean(sigmas_h, axis=0)\n",
    "```\n",
    "    \n",
    "Now that we have the mean of the measurement sigmas we can compute the covariance for every measurement sigma point, and the *cross variance* for the measurement sigma points vs the sigma points. That is expressed by these two equations\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf{P}_{zz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi_h - \\mathbf{z}_{mean}][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T} + \\mathbf{R} \\\\\n",
    "\\mathbf{P}_{xz} &= \\frac{1}{N-1}\\sum_1^N [\\boldsymbol\\chi - \\mathbf{x}^-][\\boldsymbol\\chi_h - \\mathbf{z}_{mean}]^\\mathsf{T}\n",
    "\\end{aligned}$$\n",
    "\n",
    "We can express this in Python with\n",
    "\n",
    "```python\n",
    "P_zz = 0\n",
    "for sigma in sigmas_h:\n",
    "    s = sigma - z_mean\n",
    "    P_zz += outer(s, s)\n",
    "P_zz = P_zz / (N-1) + R\n",
    "\n",
    "P_xz = 0\n",
    "for i in range(N):\n",
    "    P_xz += outer(self.sigmas[i] - self.x, sigmas_h[i] - z_mean)\n",
    "P_xz /= N-1\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computation of the Kalman gain is straightforward $\\mathbf{K} = \\mathbf{P}_{xz} \\mathbf{P}_{zz}^{-1}$.\n",
    "\n",
    "In Python this is\n",
    "\n",
    "```python\n",
    "K = np.dot(P_xz, inv(P_zz))```\n",
    "\n",
    "Next, we update the sigma points with\n",
    "\n",
    "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R]$$ \n",
    "\n",
    "Here $\\mathbf{v}_R$ is the perturbation that we add to the sigmas. In Python we can implement this with\n",
    "\n",
    "```python\n",
    "v_r = multivariate_normal([0]*dim_z, R, N)\n",
    "for i in range(N):\n",
    "    sigmas[i] += dot(K, z + v_r[i] - sigmas_h[i])\n",
    "```\n",
    "\n",
    "\n",
    "Our final step is recompute the filter's mean and covariance.\n",
    "\n",
    "```python\n",
    "    x = np.mean(sigmas, axis=0)\n",
    "    P = self.P - dot(K, P_zz).dot(K.T)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation and Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have implemented an EnKF in the `FilterPy` library. It is in many ways a toy. Filtering with a large number of sigma points gives us very slow performance. Furthermore, there are many minor variations on the algorithm in the literature. I wrote this mostly because I was interested in learning a bit about the filter. I have not used it for a real world problem, and I can give no advice on using the filter for the large problems for which it is suited. Therefore I will refine my comments to implementing a very simple filter. I will use it to track an object in one dimension, and compare the output to a linear Kalman filter. This is a filter we have designed many times already in this book, so I will design it with little comment. Our state vector will be\n",
    "\n",
    "$$\\mathbf{x} = \\begin{bmatrix}x\\\\ \\dot{x}\\end{bmatrix}$$\n",
    "\n",
    "The state transition function is\n",
    "\n",
    "$$\\mathbf{F} = \\begin{bmatrix}1&1\\\\0&1\\end{bmatrix}$$\n",
    "\n",
    "and the measurement function is\n",
    "\n",
    "$$\\mathbf{H} = \\begin{bmatrix}1&0\\end{bmatrix}$$\n",
    "\n",
    "The EnKF is designed for nonlinear problems, so instead of using matrices to implement the state transition and measurement functions you will need to supply Python functions. For this problem they can be written as:\n",
    "\n",
    "```python\n",
    "def hx(x):\n",
    "    return np.array([x[0]])\n",
    "\n",
    "def fx(x, dt):\n",
    "    return np.dot(F, x)\n",
    "```\n",
    "\n",
    "One final thing: the EnKF code, like the UKF code, uses a single dimension for $\\mathbf{x}$, not a two dimensional column matrix as used by the linear kalman filter code.\n",
    "\n",
    "Without further ado, here is the code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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i4orVKTzb1Go1kiShUCie+HvD1tYWb+/7D+gRHsyZM2fQaDTF/m0RhLuJe0Uoi4q4X+Lj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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x24e9a520ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import kf_book.book_plots as bp\n",
    "from numpy.random import randn\n",
    "from filterpy.kalman import EnsembleKalmanFilter as EnKF\n",
    "from filterpy.kalman import KalmanFilter\n",
    "from filterpy.common import Q_discrete_white_noise\n",
    "\n",
    "np.random.seed(1234)\n",
    "\n",
    "def hx(x):\n",
    "    return np.array([x[0]])\n",
    "\n",
    "def fx(x, dt):\n",
    "    return np.dot(F, x)\n",
    "    \n",
    "F = np.array([[1., 1.],[0., 1.]])\n",
    "\n",
    "x = np.array([0., 1.])\n",
    "P = np.eye(2) * 100.\n",
    "enf = EnKF(x=x, P=P, dim_z=1, dt=1., N=20, hx=hx, fx=fx)\n",
    "\n",
    "std_noise = 10.\n",
    "enf.R *= std_noise**2\n",
    "enf.Q = Q_discrete_white_noise(2, 1., .001)\n",
    "\n",
    "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
    "kf.x = np.array([x]).T\n",
    "kf.F = F.copy()\n",
    "kf.P = P.copy()\n",
    "kf.R = enf.R.copy()\n",
    "kf.Q = enf.Q.copy()\n",
    "kf.H = np.array([[1., 0.]])\n",
    "\n",
    "measurements = []\n",
    "results = []\n",
    "ps = []\n",
    "kf_results = []\n",
    "\n",
    "zs = []\n",
    "for t in range (0,100):\n",
    "    # create measurement = t plus white noise\n",
    "    z = t + randn()*std_noise\n",
    "    zs.append(z)\n",
    "\n",
    "    enf.predict()\n",
    "    enf.update(np.asarray([z]))\n",
    "    \n",
    "    kf.predict()\n",
    "    kf.update(np.asarray([[z]]))\n",
    "\n",
    "    # save data\n",
    "    results.append (enf.x[0])\n",
    "    kf_results.append (kf.x[0,0])\n",
    "    measurements.append(z)\n",
    "    ps.append(3*(enf.P[0,0]**.5))\n",
    "\n",
    "results = np.asarray(results)\n",
    "ps = np.asarray(ps)\n",
    "\n",
    "plt.plot(results, label='EnKF')\n",
    "plt.plot(kf_results, label='KF', c='b', lw=2)\n",
    "bp.plot_measurements(measurements)\n",
    "plt.plot (results - ps, c='k',linestyle=':', lw=1, label='1$\\sigma$')\n",
    "plt.plot(results + ps, c='k', linestyle=':', lw=1)\n",
    "plt.fill_between(range(100), results - ps, results + ps, facecolor='y', alpha=.3)\n",
    "plt.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be a bit difficult to see, but the KF and EnKF start off slightly different, but soon converge to producing nearly the same values. The EnKF is a suboptimal filter, so it will not produce the optimal solution that the KF produces. However, I deliberately chose $N$ to be quite small (20) to guarantee that the EnKF output is quite suboptimal. If I chose a more reasonable number such as 2000 you would be unable to see the difference between the two filter outputs on this graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Outstanding Questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of this should be considered as *my* questions, not lingering questions in the literature. However, I am copying equations directly from well known sources in the field, and they do not address the discrepancies.\n",
    "\n",
    "First, in Brown [2] we have all sums multiplied by $\\frac{1}{N}$, as in \n",
    "\n",
    "$$ \\hat{x} = \\frac{1}{N}\\sum_{i=1}^N\\chi_k^{(i)}$$\n",
    "\n",
    "The same equation in Crassidis [3] reads (I'll use the same notation as in Brown, although Crassidis' is different)\n",
    "\n",
    "$$ \\hat{x} = \\frac{1}{N-1}\\sum_{i=1}^N\\chi_k^{(i)}$$\n",
    "\n",
    "The same is true in both sources for the sums in the computation for the covariances. Crassidis, in the context of talking about the filter's covariance, states that $N-1$ is used to ensure an unbiased estimate. Given the following standard equations for the mean and standard deviation (p.2 of Crassidis), this makes sense for the covariance.\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mu &= \\frac{1}{N}\\sum_{i=1}^N[\\tilde{z}(t_i) - \\hat{z}(t_i)] \\\\\n",
    " \\sigma^2 &= \\frac{1}{N-1}\\sum_{i=1}^N\\{[\\tilde{z}(t_i) - \\hat{z}(t_i)] - \\mu\\}^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "However, I see no justification or reason to use $N-1$ to compute the mean. If I use $N-1$ in the filter for the mean the filter does not converge and the state essentially follows the measurements without any filtering. However, I do see a reason to use it for the covariance as in Crassidis, in contrast to Brown. Again, I support my decision empirically - $N-1$ works in the implementation of the filter, $N$ does not.\n",
    "\n",
    "My second question relates to the use of the $\\mathbf{R}$ matrix. In Brown $\\mathbf{R}$ is added to $\\mathbf{P}_{zz}$ whereas it isn't in Crassidis and other sources. I have read on the web notes by other implementers that adding R helps the filter, and it certainly seems reasonable and necessary to me, so this is what I do. \n",
    "\n",
    "My third question relates to the computation of the covariance $\\mathbf{P}$. Again, we have different equations in Crassidis and Brown. I have chosen the implementation given in Brown as it seems to give me the  behavior that I expect (convergence of $\\mathbf{P}$ over time) and it closely compares to the form in the linear KF. In contrast I find the equations in Crassidis do not seem to converge much.\n",
    "\n",
    "My fourth question relates to the state estimate update. In Brown we have \n",
    "\n",
    "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\mathbf{z}_{mean} + \\mathbf{v}_R]$$ \n",
    "\n",
    "whereas in Crassidis we have\n",
    "\n",
    "$$\\boldsymbol\\chi  = \\boldsymbol\\chi + \\mathbf{K}[\\mathbf{z} -\\boldsymbol\\chi_h + \\mathbf{v}_R]$$ \n",
    "\n",
    "To me the Crassidis equation seems logical, and it produces a filter that performs like the linear KF for linear problems, so that is the formulation that I have chosen. \n",
    "\n",
    "I am not comfortable saying either book is wrong; it is quite possible that I missed some point that makes each set of equations work. I can say that when I implemented them as written I did not get a filter that worked. I define \"work\" as performs essentially the same as the linear KF for linear problems. Between reading implementation notes on the web and reasoning about various issues I have chosen the implementation in this chapter, which does in fact seem to work correctly. I have yet to explore the significant amount of original literature that will likely definitively explain the discrepancies. I would like to leave this here in some form even if I do find an explanation that reconciles the various differences, as if I got confused by these books than probably others will as well."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [1] Mackenzie, Dana. *Ensemble Kalman Filters Bring Weather Models Up to Date* Siam News,  Volume 36, Number 8, October 2003. http://www.siam.org/pdf/news/362.pdf\n",
    "\n",
    "- [2]  Brown, Robert Grover, and Patrick Y.C. Hwang. *Introduction to Random Signals and Applied Kalman Filtering, With MATLAB® excercises and solutions.* Wiley, 2012.\n",
    "\n",
    "- [3] Crassidis, John L., and John L. Junkins. *Optimal estimation of dynamic systems*. CRC press, 2011."
   ]
  }
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